Análise de Multicolinearidade em Regressão

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1 
VIF – VARIATION INFLATION FACTOR 
Mede o quanto a variação de um coeficiente de regressão estimado aumenta se seus 
preditores estiverem correlacionados (multicolinear). 
 
 
 
Regra de bolso para o VIF: 
 
 
 até 1 - sem multicolinearidade 
 
 de 1 até 10 - multicolinearidade aceitável 
 
 acima de 10 - multicolinearidade problemática 
2 
TESTE DE MULTICOLINEARIDADE 
 
Teste de aceitação Teste de Farrar & Glauber 
 
 
 
H0: Ausência de Multicolinearidade 
 
 
 
 
c2 teste > c2 crítico → Rejeita H0 (Há correlação entre as variáveis) 
3 
ÍNDICE TOLERANCE 
 
 
Regra de bolso para o índice Tolerance: 
 
 
 até 1 - sem multicolinearidade 
 
 
 de 1 até 0,10 - multicolinearidade aceitável 
 
 
 abaixo de 0,10 - multicolinearidade problemática 
 
4 
House Price Size Age TOOLS / DATA ANALYSIS / Regression
1 68.70 2.05 3.43
2 54.90 1.70 11.61
3 51.50 1.47 8.31 Regression Statistics
4 71.60 1.75 0.00
5 58.40 1.94 7.41
6 40.70 1.19 31.70
7 51.70 1.56 16.10
8 71.90 1.95 2.05
9 57.10 1.60 1.74
10 58.30 1.49 2.76
11 73.50 1.91 0.00
12 58.50 1.38 0.00
13 49.10 1.55 12.61
14 67.50 1.88 2.80
15 53.70 1.60 7.08
16 50.00 1.55 18.00
EXCEL – DATA ANALYSIS CALCULATION 
 
Tools  Data Analysis  Regression 
5 
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.914
R Square 0.836
Adjusted R Square0.810
Standard Error 4.166
Observations 16
ANOVA
df SS MS F Significance F
Regression 2 1146.2 573.1 33.0 0.0
Residual 13 225.6 17.4
Total 15 1371.8
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0%Upper 95.0%
Intercept 29.42 9.99 2.94 0.011 7.84 51.00 7.84 51.00
Size 20.33 5.54 3.67 0.003 8.36 32.30 8.36 32.30
Age -0.59 0.15 -3.85 0.002 -0.92 -0.26 -0.92 -0.26
6 
EXCEL: Test for Multicollinearity by Correlation Analysis 
 High correlation between dependent variable and the independent variables is desirable. 
 
 High correlation between the independent variables is undesirable – a potential 
multicollinearity condition. 
 
Tools  Data Analysis  Correlation 
 
House Price Size Age Price Size Age
1 68.70 2.05 3.43 Price 1
2 54.90 1.70 11.61 Size 0.805 1
3 51.50 1.47 8.31 Age -0.816 -0.572 1
4 71.60 1.75 0.00
5 58.40 1.94 7.41 TOOLS / DATA ANALYSIS / Correlation
6 40.70 1.19 31.70
7 51.70 1.56 16.10
8 71.90 1.95 2.05
9 57.10 1.60 1.74
10 58.30 1.49 2.76
11 73.50 1.91 0.00
12 58.50 1.38 0.00
13 49.10 1.55 12.61
14 67.50 1.88 2.80
15 53.70 1.60 7.08
16 50.00 1.55 18.00
7 
Analyze  Regression  Linear 
SPSS – DATA ANALYSIS CALCULATION 
8 
Model Summary
.914a .836 .810 4.1657
Model
1
R R Square
Adjusted
R Square
Std. Error of
the Estimate
Predictors: (Constant), AGE, SIZEa. 
ANOVAb
1146.245 2 573.123 33.027 .000a
225.589 13 17.353
1371.834 15
Regression
Residual
Total
Model
1
Sum of
Squares df Mean Square F Sig.
Predictors: (Constant), AGE, SIZEa. 
Dependent Variable: PRICEb. 
Coefficientsa
29.420 9.990 2.945 .011
20.332 5.540 .503 3.670 .003
-.588 .153 -.527 -3.845 .002
(Constant)
SIZE
AGE
Model
1
B Std. Error
Unstandardized
Coeff icients
Beta
Standardized
Coeff icients
t Sig.
Dependent Variable: PRICEa. 
9 
Correlations
1 .805** -.816**
. .000 .000
16 16 16
.805** 1 -.572*
.000 . .020
16 16 16
-.816** -.572* 1
.000 .020 .
16 16 16
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
PRICE
SIZE
AGE
PRICE SIZE AGE
Correlat ion is signif icant at the 0.01 lev el (2-tailed).**. 
Correlat ion is signif icant at the 0.05 lev el (2-tailed).*. 
SPSS: Test for Multicollinearity by Correlation Analysis 
 High correlation between dependent variable and the independent variables is desirable. 
 
 High correlation between the independent variables is undesirable – a potential 
multicollinearity condition. 
 
Analysis  Correlate  Bivariate 
 
10 
Analysis  Regression  Linear 
Coefficients St Coef t Sig. Collinearity Statistics
B Std. Error Beta Tolerance VIF
(Constant) 29.420 9.99 2.94 0.011
SIZE 20.332 5.54 0.503 3.67 0.003 0.67 1.49
AGE -0.588 0.15 -0.527 -3.85 0.002 0.67 1.49
SPSS: Test for Multicollinearity by VIF 
De 1 até 10: 
multicolinearidade 
aceitável